curve #6380

y² + xy + y = x³ − 225697055834092775331248653514927909012x + 1304839966526367079292622346635594172566212354194928747330

a-invariants: [1, 0, 1, -225697055834092775331248653514927909012, 1304839966526367079292622346635594172566212354194928747330]
c-invariants: [10833458680036453215899935368716539632553, -1127381731078781156525075895513208044921057377077493247142165]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 17153194934093648937888015864579548144183014877220462
discriminant (Δ): 270024573229128276090006689864315816778965099908303459634493821980848652435175762095432595425899176908551239485584
Faltings height: 20.7609
naive height: 276.5504
primes of bad reduction: 2, 3, 11, 17, 31, 37, 43, 59, 97, 101, 173, 223, 283, 313, 509, 643, 811, 1669, 2441, 18353, 76631, 103183
regulator: 8142477645586.214870950454589389898295603200189571854792031695427
submitted by: apkorte
submitted at: 2026-11-01 21:17:58 UTC
last updated: 2026-11-01 21:17:58 UTC

Witness: 13 independent points log in to add more points →

(22912384715375325141, 90344151648096795702348376999)
(7775533252773607578, 4474966614248503735112065483)
(7411142680723522734, -6262919485115065915004223281)
(8359419010476971562, 1516231003151279402714485531)
(11903495092422888453, 17461398170801337815808108883)
(12209723706930009429, 19218079096910244710341616899)
(8469075908437793252277/121, 762740250152744505182392582796501/1331)
(4258252986937509593745933/1570009, 52515809699313093467398268998801438187/1967221277)
(-394298875157636929116/25, 3834828007652428883777940430238/125)
(9085588543251232962, 2060536464613842372263909971)
(202089129516245306628067149/34562641, -2764317999400973381272593688838223776179/203193766439)
(8793230338234696149, 366400939753017510036707971)
(789796717265386896140685242121/92084937025, -1670329765572057568976981467209050917378459/27943634564921375)

Commentary

From a public submission branch of the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, branch submissions/1823cd1b-9025-4448-aa7c-3f8e2c989879, file submission/board/x312-p-16288-q41497.ec; pull request #63, closed without merging), where it is recorded as a challenge participant's own find: the fibre T = -16288/41497 of the Z/2xZ/2 K3 fibration x312. Not our discovery. Posted by apkorte with Claude (Anthropic), which moved the points to the minimal model and checked their independence.

last edited by apkorte at 2026-11-01 21:17:58 UTC · history